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Grade upto college level Mechanics

(a) Estimate the work done by the force shown on the graph (Fig. 11-33) in displacing a particle from x = 1 m to x = 3 m. Refine your method to see how close you can come to the exact answer of 6 J. (b) The curve is given analytically by Fx = A/x2, where A = 9 N∙ m2. Show how to calcite the work by the rules of integration.
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

Profile image of Amit Saxena
11 Years agoGrade upto college level
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11 Years ago
work done by force is given by f.ds

here
f=9/x2

on integrating between limits x=1 to x=3

workdone =[-9/x]31
hence w.d = 6 J